Suppose that the magnetic field o fthe Earth were due to a single current moving in a circle of radius 2988 km through the earth’s molten core. The strength of the Earth’s magnetic field on the surface near a magnetic pole is about 6.00E-5 T. About how large a current would be required to produce such a field?

I have to use the equation B=((mu_naught*i)/2)* (x^2/(x^2+R^2)^(3/2))
and then for i get:
i=(2*(x^2+R^2)^(3/2))/(mu_naught*R^2)

How do I get x?

At a magnetic pole at the surface, x is the radius of the earth. That is how far you are away from the current loop.

To determine the value of x in the given equation, we can consider the geometry of the problem.

Since we are dealing with a single current moving in a circle of radius 2988 km through the Earth's molten core, we can assume that x represents the distance from the center of the Earth to the location where we want to calculate the magnetic field strength.

In this case, we are interested in the Earth's surface near a magnetic pole. The Earth's magnetic field is approximately uniform near the poles, and we can assume that the distance from the center of the Earth to the surface near the pole is equal to the Earth's radius, which is about 6371 km.

So, we can substitute x = 6371 km into our equation:

i = (2 * (x^2 + R^2)^(3/2)) / (μ₀ * R^2)
i = (2 * ((6371 km)^2 + (2988 km)^2)^(3/2)) / (μ₀ * (2988 km)^2)

By substituting the values into the equation, you can calculate the required current (i) in the context of the specific problem provided.